Cosmic inflation has been identified as the most appealing theory removing shortcomings of the hot big bang model and also the main reliable approach for structure formation of the universe. Furthermore, primordial gravitational waves are produced through primordial perturbations and they could be observed, in principle, in the stochastic background [1]}, [2]}, [3]}, [4]}, [5]}, [6]}. Based on the standard formalism, a single scalar field (inflaton) can drive inflation, and then by decaying at the last stage of the period, inflation will be terminated throughout a reheating process [7]}, [8]}. Several inflationary models are equipped with the slow-roll approximation which says inflaton rolls slowly down from the top of potential to the minimum point with a canonical kinetic term. For a long time, the single field inflationary models have been investigated in literature in detail so that by comparing with the Planck data, some of them are restricted or even ruled out [9]}. However, some models are still viable with the recent high precision observations [10]}, [11]}, [12]}, [13]}. One of the most significant properties of these models is that they do not present any non-Gaussianity in their primordial spectrum because of uncorrelated modes of the spectrum [14]}. In such a case, if the future observations predict non-Gaussianities in the perturbations spectrum, then this class of models will be felt in serious uncertainty. In order to remove the expected obstacles, a new class of inflationary models has been suggested in which inflaton is rolling down with a constant rate during inflation [15]}, [16]}, [17]}. This means that \(\ddot{\varphi }\)  is non-negligible and can be expressed as
\(\ddot{\varphi }=\beta H\dot{\varphi }\) 
